Probability of Normal Distribution

1. Management of an airline knows that 0.5% of the airline's passengers lose their luggage on domestic flights. Management also know that the average value claimed for a lost piece of luggage on domestic flights is $600.00. The company is considering increasing fares by an appropriate amount to cover expected compensation to passengers who lose their luggage. By how much should the airline increase fares? Why? Explain, using the ideas of a random variable and its expectation.

2. A large shipment of computer chips is known to contain 10% defective chips. If 100 chips are randomly selected, what is the expected number of defective ones? What is the standard deviation of the number of defective chips? Use Chebyshev's theorem to give bounds such that there is at least a 0.75 chance that the number of defective chips will be within the two bounds.

3. A mainframe computer in a university crashes on the average 0.71 times in a semester.

a. What is the probability that it will crash at least two time sin a given semester?
b. What is the probability that it will not crash at all in a given semester?
c. The MIS administrator wants to increase the probability of no crash at all in a semester to at least 90%. What is the largest u (mu) that will achieve this goal?

4. A recent survey published in Business Week concludes that Gatorade commands an 80% share of the sports drink market versus 11% for Coco-Cola's Power Ade and 3% for Pepsi's All Sport. A market research firm wants to conduct a new taste test for which it needs Gatorade drinkers. Potential participants for the test are selected by random screening of drink users to find Gatorade drinkers. What is the probability that

a. The first randomly selected drinker qualifies
b. Three soft drink users will have to be interviewed to find the first Gatorade drinker.